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The sharpness of detail in a television picture is directly dependent upon the capability of the transmitter for the transmission of abrupt changes in picture half tone. A suitable test signal is a square wave of sufficiently long period. Rules are deduced for the evaluation of the subjective sharpness to be expected in transmitted pictures and may be applied when the square-wave response of the transmitting apparatus is known. Rapid chart methods have been devised for (1) the analysis of a square-wave output into sine-wave amplitude and phase response and (2) the synthesis of a square-wave response from a given set of amplitude and phase characteristics. Analysis furnishes an immediate solution to the familiar but troublesome problem of finding the sine-wave characteristics of television apparatus. The four aspects of the application of square waves to television, i.e., measurement, analysis, synthesis, and evaluation, are presented as a basis for a unified and complete technique. The authors hope that this paper will be a contribution to the general problem of working out electrical specifications for television transmitters and other television apparatus, giving information regarding the steepness of rise and the amplitude of overswing of the square-wave response.